论文标题
关于粘性可压缩液中消失的刚体问题
On the vanishing rigid body problem in a viscous compressible fluid
论文作者
论文摘要
在本文中，我们研究了一个小刚体在粘性压缩液中的相互作用。该系统占据了一个有限的三维域。它允许自由移动的对象遵循牛顿的定律。我们表明，随着物体的尺寸收敛到零，系统流体和刚体的体内在质量和惯性动量的一些轻度下限下会收敛到可压缩的Navier-Stokes系统。在可压缩情况下流体结构相互作用的情况下，这是同质化的第一个结果。作为推论，我们以$γ\ geq 6 $在可压缩流体中消失的障碍物影响的结果稍微改善了结果。
In this paper we study the interaction of a small rigid body in a viscous compressible fluid. The system occupies a bounded three dimensional domain. The object it allowed to freely move and its dynamics follows the Newton's laws. We show that as the size of the object converges to zero the system fluid plus rigid body converges to the compressible Navier-Stokes system under some mild lower bound on the mass and the inertia momentum. It is a first result of homogenization in the case of fluid-structure interaction in the compressible situation. As a corollary we slightly improved the result on the influence of a vanishing obstacle in a compressible fluid for $ γ\geq 6$ .
